Torque on Current Loop, Magnetic Dipole

The magnetic dipole moment, or the strength of a magnetic dipole, can be regarded as a measure of a dipole’s capacity to align itself with a particular external magnetic field. The size of the dipole moment in a uniform magnetic field is proportional to the maximum amount of torque applied to the dipole, which occurs when the dipole is at right angles to the magnetic field. The maximum amount of torque induced by magnetic force on a dipole that emerges per unit value of the surrounding magnetic field in a vacuum is known as the magnetic dipole moment, or simply the magnetic moment.

Explain Torque

Since Torque is a twisting force, it leads to rotation. The point where the object rotates is known as the axis of the rotation.

The formula for the Torque is τ = F×r

Here τ  is the Torque, F = force applied, and r = the total distance between applied force and centre of the rotation.

Torque on Current Loop, Magnetic Dipole

Imagine a rectangular loop in a way that it carries the magnitude current I. When this rectangular loop is placed in the magnetic field, it does not experience a net force but a torque. Similar to electric dipoles. Consider that the rectangular loop is in the plane with the magnetic field B. there is no external force exerted on loop arms that are parallel to the magnet. However, the arms that are placed perpendicularly to magnets experience force donated as F₁.

F₁ = IbB

Similarly, a different expression can be written for force F₂ as.

F₂ = IbB = F₁

We see that the net force on the loop is zero and the torque on the loop is given by,

Torque (τ) = F₁.a/2 + F₂.a/2

= IbB.a/2 + IbB.a/2 = I(ab)B = IAB

Here, ab is the total area of the rectangle. Also, the Torque is supposed to rotate the loop in the opposite direction or anti-clockwise direction.

In the first case, the loop’s plane was along with the magnetic field; however, in this case, the loop’s plane was not along with the magnetic field. Say the angle between the normal to the coil and the field is donated by θ. We will notice that the arms force will be the same in magnitude and act opposite to one another. As mentioned, these forces are collinear and equal opposite at all points; they can cancel each other’s effects which results in Torque or zero-force. These arm forces are donated by F1 and F2 and are opposite in direction and equal in magnitude.

It is given by,

F₁ = F₂ = IbB

These forces are not collinear and thus act as a couple exerting a torque on the coil. The magnitude of the torque can be given by,

Torque (τ) = F₁.a/2 sinθ + F₂.a/2sinθ

= IabBsinθ

= IABsinθ

Rectangular loop carrying a steady current :

Rectangular loop carrying a steady current in the plane of the loop.

• The long straight wire and side AB both carry current in the same direction. Therefore, they will attract.
• Because the long straight wire and the side CD carry current in different directions, they repel each other.
• The force on the BC side will be equal to and opposite to the force on the DA side.
• Because CD is further away from the wire than AB, the attraction force on AB will be greater than the repulsion force on CD.
• As a result, the loop ABCD will experience a net force of attraction and will move towards the wire.

Circular current loop as a magnetic dipole

The attached graphic depicts magnetic field lines caused by a current-carrying wire. The field lines mimic magnet field lines. As a result, it acts as a magnetic dipole. Its field lines can be used to locate its poles (Field lines leave the magnet from the north pole and enter from the south pole).

Magnetic dipole moment of a revolving electron

By definition, the majority of elementary particles are magnetic dipoles. The electron, for example, is a magnetic dipole with a Spin Magnetic Dipole moment. Because the electron has neither an area A (it is a point object) nor does it rotate around itself, this magnetic moment is critical to its existence.

According to Neil Bohr’s atom model, a negatively charged electron orbits a positively charged nucleus in a circular orbit of radius r. A revolving electron in a confined channel makes up an electric current. The electron’s anti-clockwise motion causes a conventional current to flow in the clockwise direction.

Magnetic Dipole

It’s similar to an electric dipole in electrostatics. We have two magnetic poles, the north and south poles, which are separated by a distance. The difference is that while individual positive and negative electric charges can be observed in nature, magnetic monopoles, i.e. individual north and south poles, have never been found in nature. As a result, we come to the conclusion that magnetic monopoles do not exist. They exist in the form of a magnetic dipole at all times.

Magnetic Dipole Moment

In electrostatics, the electrical moment is defined as the product of the magnitude of charge and distance between both the costs. Similarly, for a magnet, we will define the dipole moment because of the product of pole strength (p) of any of the poles and also the magnetic length (effective distance between both the poles) of the magnet.

Vactor μ=p.vactor L

Pole strength determines the power of a magnet to form a field of force. The direction of the dipole moment inside the magnet is from the pole to the North Pole.

Conclusion

We learned a little bit about magnets and magnetic fields in this post, as well as the magnetic moment of a permanent magnet and a current-carrying loop, and how an external magnetic field affects loop carrying current. The study of magnetic dipole moments is crucial for understanding the influence of a magnetic field on a loop or any other magnet since it aids in determining loop torque and magnetic energy.

A bar magnet’s magnetic moment is equal to pL.

A current-carrying loop’s magnetic moment is equal to IA.